Match:

A. r(1997)−r(1992)
B. ∫19921997r′(t)dt
C. r(1997)
D. ∫19921997r(t)dt
E. [ r(1997)−r(1992)/1997−1992]

and interpretations:

A. Average rate of change of the debt rate between 1992 and 1997
B. Change in debt rate between 1992 and 1997
C. Increase in debt between 1992 and 1997
D. Debt of the country in 1997
E. Rate of debt in 1997

To correctly match the expressions and their interpretations, let's analyze each expression and interpretation:

A. r(1997)−r(1992)
This expression calculates the difference in the debt rate between 1997 and 1992.

Interpretation: Average rate of change of the debt rate between 1992 and 1997

B. ∫19921997r′(t)dt
This expression represents the integral of the derivative of the debt rate function from 1992 to 1997. In other words, it calculates the total change in the debt rate over that time period.

Interpretation: Change in debt rate between 1992 and 1997

C. r(1997)
This expression gives the debt rate specifically in the year 1997.

Interpretation: Rate of debt in 1997

D. ∫19921997r(t)dt
This expression represents the integral of the debt rate function from 1992 to 1997. It calculates the total amount of debt accumulated over that time period.

Interpretation: Debt of the country in 1997

E. [ r(1997)−r(1992)/1997−1992]
This expression calculates the average rate of change of the debt rate between 1992 and 1997. It is obtained by dividing the difference in debt rate between those two years by the difference in the years themselves.

Interpretation: Average rate of change of the debt rate between 1992 and 1997

To summarize the matches:

A. Average rate of change of the debt rate between 1992 and 1997
B. Change in debt rate between 1992 and 1997
C. Rate of debt in 1997
D. Debt of the country in 1997
E. Average rate of change of the debt rate between 1992 and 1997